Padding bits in unsigned integers and bitwise oper

Question

I have a lot of code that performs bitwise operations on unsigned integers. I wrote my code with the assumption that those operations were on integers of fixed width without any padding bits. For example an array of 32-bit unsigned integers of which all 32 bits available for each integer.

I'm looking to make my code more portable and I'm focused on making sure I'm C89 compliant (in this case). One of the issues that I've come across is possible padded integers. Take this extreme example, taken from the GMP manual:

However on Cray vector systems it may be noted that short and int are always stored in 8 bytes (and with sizeof indicating that) but use only 32 or 46 bits. The nails feature can account for this, by passing for instance 8*sizeof(int)-INT_BIT.

I've also read about this type of padding in other places. I actually read of a post on SO last night (forgive me, I don't have the link and I'm going to cite something similar from memory) where if you have, say, a double with 60 usable bits the other 4 could be used for padding and those padding bits could serve some internal purpose so they cannot be modified.

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So let's say for example my code is compiled on a platform where an unsigned int type is sized at 4 bytes, each byte being 8 bits, however the most significant 2 bits are padding bits. Would UINT_MAX in that case be 0x3FFFFFFF (1073741823)?

#include <stdio.h>
#include <stdlib.h>

/* padding bits represented by underscores */
int main( int argc, char **argv )
{
    unsigned int a = 0x2AAAAAAA; /* __101010101010101010101010101010 */
    unsigned int b = 0x15555555; /* __010101010101010101010101010101 */
    unsigned int c = a ^ b; /* ?? __111111111111111111111111111111 */
    unsigned int d = c << 5; /* ??  __111111111111111111111111100000 */
    unsigned int e = d >> 5; /* ?? __000001111111111111111111111111 */

    printf( "a: %X\nb: %X\nc: %X\nd: %X\ne: %X\n", a, b, c, d, e );
    return 0;
}

• Is it safe to XOR two integers with padding bits?
• Wouldn't I XOR whatever the padding bits are?

I can't find this behavior covered in C89.

Furthermore is the c variable guaranteed to be 0x3FFFFFFF or if for example the two padding bits were both on in a or b would c be 0xFFFFFFFF?

Same question with d and e. Am I manipulating the padding bits by shifting? I would expect to see this below, assuming 32 bits with the 2 most significant bits used for padding, but I want to know if something like this is guaranteed:

a: 2AAAAAAA
b: 15555555
c: 3FFFFFFF
d: 3FFFFFE0
e: 01FFFFFF

Also are padding bits always the most significant bits or could they be the least significant bits?

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EDIT 12/19/2010 5PM EST: Christoph has answered my question. Thanks!
I had also asked (above) whether padding bits are always the most significant bits. This is cited in the rationale for the C99 standard, and the answer is no. I am playing it safe and assuming the same for C89. Here is specifically what the C99 rationale says for §6.2.6.2 (Representation of Integer Types):

Padding bits are user-accessible in an unsigned integer type. For example, suppose a machine uses a pair of 16-bit shorts (each with its own sign bit) to make up a 32-bit int and the sign bit of the lower short is ignored when used in this 32-bit int. Then, as a 32-bit signed int, there is a padding bit (in the middle of the 32 bits) that is ignored in determining the value of the 32-bit signed int. But, if this 32-bit item is treated as a 32-bit unsigned int, then that padding bit is visible to the user’s program. The C committee was told that there is a machine that works this way, and that is one reason that padding bits were added to C99.

Footnotes 44 and 45 mention that parity bits might be padding bits. The committee does not know of any machines with user-accessible parity bits within an integer. Therefore, the committee is not aware of any machines that treat parity bits as padding bits.

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EDIT 12/28/2010 3PM EST: I found an interesting discussion on comp.lang.c from a few months ago.

• Bitwise Operator Effects on Padding Bits (VelocityReviews reader)
• Bitwise Operator Effects on Padding Bits (Google Groups alternate link)

One point made by Dietmar which I found interesting:

Let's note that padding bits are not necessary for the existence of trap representations; combinations of value bits which do not represent a value of the object type would also do.

Answer 1

Bitwise operations (like arithmetic operations) operate on values and ignore padding. The implementation may or may not modify padding bits (or use them internally, eg as parity bits), but portable C code will never be able to detect this. Any value (including UINT_MAX) will not include the padding.

Where integer padding might lead to problems on is if you use things like sizeof (int) * CHAR_BIT and then try to use shifts to access all these bits. If you want to be portable, either only use (unsigned) char, fixed-sized integers (a C99 addition) or determine the number of value-bits programatically. This can be done at compile-time with the preprocessor by comparing UINT_MAX against powers of 2 or at runtime by using bit-operations.

edit:

C90 does not mention integer padding at all, but as far as I can tell, 'invisible' preceding or trailing integer padding bits shouldn't violate the standard (I didn't go through all relevant sections to make sure this is really the case, though); there probaby are problems with mixed padding and value bits as mentioned in the C99 rationale because otherwise, the standard would not have needed to be changed.

As to the meaning of user-accessible: Padding bits are accessible insofar as you can alwaye get at any bit of foo (including padding) by using bit-operations on ((unsigned char *)&foo)[…]. Be careful when modifying the padding bits, though: the result won't change the value of the integer, but might create be a trap-representation nevertheless. In case of C90, this is implicitly unspecified (as in not mentioned at all), in case of C99, it's implementation-defined.

This was not what the rationale quotation was about, though: the cited architecture represents 32-bit integers via two 16-bit integers. In case of unsigned types, the resulting integer has 32 value bits and a precision of 32; in case of signed integers, it only has 31 value bits and a precision of 30: one of the sign bits of the 16-bit integers is used as the sign bit of the 32-bit integer, the other one is ignored, thus creating a padding bit surrounded by value bits. Now, if you access a 32-bit signed integer as an unsigned integer (which is explicitly allowed and does not violate the C99 aliasing rules), the padding bit becomes a (user-accessible) value bit.